I'm not necessarily disagreeing with that - I don't think even a Roman military historian necessarily would. And it is true that Civ offers some radically ahistorical unit matchups. However, this would be first off be an ahistorical matchup of 'famous' UUs, flagship civ units, and it would create a new best UU. It would also make the Mongol UB overpowered.
Meanwhile, in historical terms - which for civ are generally totally irrelevant, the 'history argument. Although it is not -unreasonable- to say that Mongols would have whipped the legions, the historical evidence we have - Romans against horse archers, Mongols against medieval knights - is not not a conclusive test of how disciplined heavy infantry with an engineering focus would have performed against superlative horse archers; particularly once the Romans had some experience against them.
Or to make a different argument, Republican Rome sure knew how to raise armies; they're the kind of state that kicks your ass at Zama 14 years after you Cannae them.
Well, I am a Roman military historian!
I pretty much agree with you on all your points.
My view is that the Mongols were the greatest army in history (as first postulated by military historian Liddell Hart). The Romans were a great army nation for a very, very long time. As you said, the Romans had large pools of men to recover mistakes, and learned fast fro what went wrong.
As you said, comparing there military strength is hard because they are based on so many factors, like wealth, terrain, etc. along with the usual leadership, organization, etc.
The Mongols were superior to all of the other nomad armies before them, in terms of organization, skill, and training. The Mongols were masters of intelligence, and were ridiculously patient. They would send spies ahead for years to gather intelligence.
What really moved the Mongols above all other nomad armies was their use of the Chinese infrastructure. They incorporated Chinese engineers and learn their tricks. So, unlike other nomad armies, the Mongols learned siege craft.
Despite these differences, a clash between the Romans and the Mongols would probably go as Rome did against other cavalry armies. Rome had two historic enemies long-standing cavalry enemies; the Parthians, and then their conquerers, the Persians.
The Romans always had trouble with the Parthians. In the plains of the East, the battle of Carrhae always loomed large to the Romans. Mark Antony tried to avenge Crassus death, and his defeat by the Parthians is the principle reason that Octavian surpassed him. (Caesar planned a campaign against Parthia, but was assassinated before it occurred).
Over the next few hundred years, it became obvious that Rome was always stronger then Parthia, but they had to be careful in the open -- they couldn't handle Parthian mobility.
But, in 227AD, the Persians overthrew the Parthians, and now Rome had an enemy of tremendous strength. The Persians were not just strong militarily, but had a powerful culture, and a central taxation system. The destruction of Antioch by the Persians may have been the greatest blow Rome ever suffered (far greater than the sack of Rome by Alaric in 410).
Rome and Persia both finally recognized that they couldn't defeat each other. Rome was of course all around stronger, but they couldn't be stronger on the Eastern front alone. And, of course, in the open, the Persian cavalry would be superior.
Ironically, Rome delivered a death blow to Persia under Heraclius in the early 7th century. However, the conflict greatly weakened both kingdoms, and the whole east fell to the Arabs. By then, though, the eastern Romans were moving toward a cavalry army also.
So, where does that leave us with Rome and the Mongols? The Mongols were SUPREME in open terrain. They were GOOD in other terrain -- the nearly beat Japan with effectively most of their fleet destroyed, and were stuck on the beaches against a very skilled enemy, and amazingly almost won.
The Romans were strongest where heavy infantry can be deployed. The Romans also became masters of the sea. As you pointed out, the key to their overcoming their lack of mobility was their unbelievable field fortifications.
So, my view is that Mongols vs. Rome would be a classic one of style. In the open, the Mongols rule. In restricted terrain, it's the Romans. At sea, its not a contest. Rome was best whent hey could 'set-up' and use their engineering prowess. The biggest weakenss the Romans faced was poor communcations. The Mongols, of course, were supreme her.
Remember, though, that the Mongols were MUCH, MUCH more skilled than the Persians, Huns, or nomad armies that the Romans faced. It's probably lucky for them that they didn't have to deal with the Mongols.
Gibbon tals about this somewhat at the end of DFRE but he isn't as knowledgable about the Mongols.
Best wishes,
Breunor